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Risk Assessment

Radionuclide Decay Chain

Enter current activity for Parent (A0)

This value is measured activity in pCi, Bq, or any fraction thereof. Results will be given in the same units.

Enter time (T) (years or fractions of years in the future)

Assume no additional contribution from the parent during this interval.


Select Parent

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Radioactive decay occurs by various decay modes that emit energy in the form of ionizing radiation. When a radionuclide decays, it can transform into one or more different decay products. The radionuclides continuously transform into new decay products until they reach a stable state and are no longer radioactive. The series of decay products created to reach this balance is called the decay chain.

The activity at time T can be quantified for each member of the chain if the starting amount of activity (A0) for the parent is known. For linear decay chains this calculation is straight-forward using decay constants. For more complex chains, where many progeny are formed with multiple branches, this calculation becomes more difficult.

This tool can predict the activity, after a period of time, given a current measurement of activity A0 for the chain parent. A plot is provided to show the simultaneous decay rates and ingrowth, as well as a table of activities for each chain member at time T. The activities can then be used to compare to various Preliminary Remediation Goals (PRGs), Dose Compliance Concentrations (DCCs), and calculate risk or dose.

ORNL 2020 presents the methods used to create this decay chain tool. Below is a brief description.

The mathematical model used to calculate abundance and activity as a function of time is called the Bateman equation. A unique C++ Bateman solver was written to calculate the relative activity of the complete decay chain for all 1252 radionuclides identified in ICRP Publication 107 (ICRP 2007). In addition, a Python solution was developed using the Chebyshev Rational Approximation Method (CRAM). The results are stored as unit activity files (UAFs) for access by the calculators. The user entered A0 for the chain parent is multiplied by the UAF values to give the state of the chain at time T.

Decay Modes

α = Alpha decay is a form of radioactive decay in which an atomic nucleus ejects an alpha particle through the electromagnetic force and transforms into a nucleus with mass number 4 less and atomic number 2 less.

β- = Beta minus decay is a type of radioactive decay in which an electron is emitted.

EC = Electron capture is a decay mode for isotopes that will occur when there are too many protons in the nucleus of an atom, and there isn't enough energy to emit a positron; however, it continues to be a viable decay mode for radioactive isotopes that can decay by positron emission. If the energy difference between the parent atom and the daughter radionuclide is less than 1.022 MeV, positron emission is forbidden and electron capture is the sole decay mode.

β+ = Beta plus decay is a type of radioactive decay in which a positron is emitted. In beta plus decay, a proton is converted to a neutron via the weak nuclear force and a positron and a neutrino are emitted.

IT = Isomeric transition is a radioactive decay process that occurs in an atom where the nucleus is in an excited meta-state (e.g. following the emission of an alpha or beta particle). The extra energy in the nucleus is released by the emission of a gamma ray, returning the nucleus to the ground state. This process is similar to a gamma emission but differs in that it involves excited meta-states.

SF = Spontaneous fission is a form of radioactive decay characteristic of very heavy isotopes, and is theoretically possible for any atomic nucleus whose mass is greater than or equal to 100 amu (elements near ruthenium). In practice, however, spontaneous fission is only energetically feasible for atomic masses above 230 amu (elements near thorium). Spontaneous fissions release neutrons as all fissions do, so radioisotopes for which spontaneous fission is a nonnegligible decay mode may be used as neutron sources.

IC = Internal conversion is a radioactive decay process where the gamma ray emitted from a nucleus is photoelectrically absorbed by one of the most tightly bound electrons causing it to be ejected from the atom. After the ejection of the internal conversion electron, the vacancy is filled by another shell electron with a corresponding emission of one or several x-rays or Auger electrons.

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